Under what circumstances or axioms do spheres (the shape) have infinite surface area?

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• LifeInMultipleChoice@lemmy.world ⁨2⁩ ⁨days⁩ ago

  I would assume if and only if the radio is is infinite

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  • sopularity_fax@sopuli.xyz ⁨2⁩ ⁨days⁩ ago

    U’d think, right?!

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    • LifeInMultipleChoice@lemmy.world ⁨2⁩ ⁨days⁩ ago

      I read it as surface area, thus being the amount of space on the sphere itself.

      A=4πr2 is the formula if I remember correctly, so I just figure only r can be altered to match infinity

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    • Knock_Knock_Lemmy_In@lemmy.world ⁨1⁩ ⁨day⁩ ago

      Math is weird. You can have infinite circumference but finite radius.

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• Zwuzelmaus@feddit.org ⁨1⁩ ⁨day⁩ ago

  If the radius is infinite

  If the radius is >0 and the definition of sphere is used in infinite-dimensional space.

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• loppy@fedia.io ⁨1⁩ ⁨day⁩ ago

  Planes can be thought of as spheres of infinite radius, and have infinite surface area. This point of view is very natural in conformal geometry.

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• ch00f@lemmy.world ⁨2⁩ ⁨days⁩ ago

  en.wikipedia.org/wiki/Banach–Tarski_paradox

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  • mumblerfish@lemmy.world ⁨2⁩ ⁨days⁩ ago

    one can further prove that the sphere S**n−1 can be partitioned into as many pieces as there are real numbers (that is, {isplaystyle 2^{leph {0}}}pieces)

    Would the answer to OP be some argument along the lines of defining the surface area of the ball as the sum of the partitioned balls surface areas then?

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    • ch00f@lemmy.world ⁨2⁩ ⁨days⁩ ago

      IDK what OP is even going on about. This just seemed relevant.

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• Kolanaki@pawb.social ⁨2⁩ ⁨days⁩ ago

  Under the definition of what a circle is…?

  It’s a polygon with infinite sides.

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  • TonyTonyChopper@mander.xyz ⁨2⁩ ⁨days⁩ ago

    Ok but the sum of the infinite sides is a finite value

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  • sbeak@sopuli.xyz ⁨1⁩ ⁨day⁩ ago

    sphere != circle

    Sphere is like a ball (3D), while circles are like those round coasters for drinks (flat)

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    • Kolanaki@pawb.social ⁨1⁩ ⁨day⁩ ago

      Okay, and your point is? I did not describe a sphere.

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  • TonyTonyChopper@mander.xyz ⁨2⁩ ⁨days⁩ ago

    Ok but the sum of the lengths of these infinite sides is a finite value

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    • Kolanaki@pawb.social ⁨2⁩ ⁨days⁩ ago

      If OP just means the size of the entire inside of the circle, then it would need an infinite radius, too.

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